Related papers: Subelliptic Estimates for Quadratic Differential O…
We study discrete spectrum of self-adjoint Weyl pseudodifferential operators with discontinuous symbols of the form $1_\Omega \phi$ where $1_\Omega$ is the indicator of a domain in $\Omega\subset\mathbb R^2$, and $\phi\in C^\infty_0(\mathbb…
We develop a geometric framework for Weyl quantization on pseudo-Riemannian manifolds, in which pseudodifferential operators act on sections of vector bundles equipped with arbitrary connections. We construct the associated star product and…
We study the twisted Weyl symbol of metaplectic operators; this requires the definition of an index for symplectic paths related to the Conley-Zehnder index. We thereafter define a metaplectically covariant algebra of pseudo-differential…
In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable…
We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in $L^2$ spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate…
The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…
We aim at extending the definition of the Weyl calculus to an infinite dimensional setting, by replacing the phase space $ \mathbb{R}^{2n}$ by $B^2$, where $(i,H,B)$ is an abstract Wiener space. A first approach is to generalize the…
For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
In this article we provide global subelliptic estimates for the linearized inhomogeneous Boltzmann equation without angular cutoff, and show that some global gain in the spatial direction is available although the corresponding operator is…
In this note first we study the Weyl operators and Weyl S-spectrum of a bounded right quaternionic linear operator, in the setting of the so-called S-spectrum, in a right quaternionic Hilbert space. In particular, we give a characterization…
In this paper we study rank two commuting ordinary differential operators with polynomial coefficients and the orbit space of the automorphisms group of the first Weyl algebra on such operators. We prove that for arbitrary fixed spectral…
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding…
We give explicit formulas for the Berezin symbols and the complex Weyl symbols of the metaplectic representation operators by using the holomorphic representations of the Jacobi group. Then we recover some known formulas for the symbols of…
We characterize geometrically the regularizing effects of the semigroups generated by accretive non-selfadjoint quadratic differential operators. As a byproduct, we establish the subelliptic estimates enjoyed by these operators, being…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
For a quasi-split Satake diagram, we define a modified $q$-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding $\imath$quantum group. In other words, we provide a differential operator approach to…
We consider one-point commuting difference operators of rank one. The coefficients of these operators depend on a functional parameter, shift operators being included only with positive degrees. We study these operators in the case of…
We characterize the entropy and minimax risk of a broad class of compact pseudodifferential operators. Under suitable decay and regularity conditions on the symbol, we combine a Weyl-type asymptotic relation between the eigenvalue-counting…
The aim of this article is to prove a Beals type characterization theorem for pseudodifferential operators in Wiener spaces. The definition of pseudodifferential operators in Wiener spaces and a Calder\'on-Vaillancourt type result appear in…